3d static rigid body equilibrium problem

We could say it's 'close enough for government work.' We would have to conclude that this low margin of experimental error reflects an experiment with excellent results. The difference between the actual results and the expected results is due to the error incurred when measuring force A and force B. But what about the 0.1 N difference between rightward and leftward forces and the 0.2 N difference between the upward and downward forces? Why do the components of force only nearly balance? The sample data used in this analysis are the result of measured data from an actual experimental setup. The vector sum of all the forces is ( nearly) equal to 0 Newton. An analysis of the vertical components show that the sum of the upward components of A + B nearly balance the downward component of C. An analysis of the horizontal components shows that the leftward component of A nearly balances the rightward component of B. The data in the table above show that the forces nearly balance. The magnitude and direction of each component for the sample data are shown in the table below the diagram. For vectors A and B, the vertical components can be determined using the sine of the angle and the horizontal components can be analyzed using the cosine of the angle. The diagram below shows vectors A, B, and C and their respective components. Once the components are known, they can be compared to see if the vertical forces are balanced and if the horizontal forces are balanced. This is what we expected - since the object was at equilibrium, the net force (vector sum of all the forces) should be 0 N.Īnother way of determining the net force (vector sum of all the forces) involves using the trigonometric functions to resolve each force into its horizontal and vertical components. Sample data for such a lab are shown below.įor most students, the resultant was 0 Newton (or at least very close to 0 N). (Recall that the net force is 'the vector sum of all the forces' or the resultant of adding all the individual forces head-to-tail.) Thus, an accurately drawn vector addition diagram can be constructed to determine the resultant. Thus, if all the forces are added together as vectors, then the resultant force (the vector sum) should be 0 Newton. If the object is at equilibrium, then the net force acting upon the object should be 0 Newton.

The object is a point on a string upon which three forces were acting. The state of the object is analyzed in terms of the forces acting upon the object. A common physics lab is to hang an object by two or more strings and to measure the forces that are exerted at angles upon the object to support its weight.

If an object is at rest and is in a state of equilibrium, then we would say that the object is at 'static equilibrium.' 'Static' means stationary or at rest. This too extends from Newton's first law of motion.

in motion and continuing in motion with the same speed and direction.

But having an acceleration of 0 m/s/s does not mean the object is at rest. This extends from Newton's first law of motion. Objects at equilibrium must have an acceleration of 0 m/s/s.

Thus, the net force is zero and the acceleration is 0 m/s/s.

Balanced is the key word that is used to describe equilibrium situations. If an object is at equilibrium, then the forces are balanced. The 50 N force is not equal to the 30 N force. Note that the two objects are at equilibrium because the forces that act upon them are balanced however, the individual forces are not equal to each other. Consider the two objects pictured in the force diagram shown below. This however does not necessarily mean that all the forces are equal to each other. The forces are considered to be balanced if the rightward forces are balanced by the leftward forces and the upward forces are balanced by the downward forces. When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium.

3d static rigid body equilibrium problem